1. **Problem 1: Sunny and Rainy Days** Last month, there were 4 sunny days for every rainy day, and the month had 30 days total. We want to find how many days were rainy. 2. **Set up the ratio and equation:** The ratio of sunny to rainy days is $4:1$. Let the number of rainy days be $x$. Then the number of sunny days is $4x$. 3. **Write the total days equation:** $$4x + x = 30$$ 4. **Simplify and solve:** $$5x = 30$$ $$x = \frac{30}{5} = 6$$ So, there were 6 rainy days. 5. **Explanation:** Since for every rainy day there are 4 sunny days, the total days are split into 5 equal parts. Dividing 30 by 5 gives the size of one part (rainy days), which is 6. --- 6. **Problem 2: Noah's Bike Race Time** Noah can ride 32 miles in 160 minutes. We want to find how long it will take him to ride 100 miles at the same rate. 7. **Using Table A:** Distance (miles): 32, 1, 100 Elapsed time (minutes): 160, ?, ? Find time for 1 mile: $$\text{Time per mile} = \frac{160}{32} = 5 \text{ minutes}$$ Then time for 100 miles: $$100 \times 5 = 500 \text{ minutes}$$ 8. **Using Table B:** Distance (miles): 32, 96, 100 Elapsed time (minutes): 160, 4, ? Note: The 4 minutes for 96 miles is inconsistent with the rate (since 96 miles should take longer than 160 minutes). This table seems incorrect or has a typo. 9. **Conclusion:** Table A works better because it uses a consistent rate and allows us to calculate the time per mile and then scale up to 100 miles. --- **Final answers:** - Rainy days: $6$ - Time to finish 100-mile race: $500$ minutes